Method and system for wavelet based detection of colon polyps

ABSTRACT

A method of identifying colon polyps in a digital volume, wherein the volume includes a plurality of values corresponding to a domain of points in a 3D space, is provided. The method includes selecting a mother wavelet scaling function that corresponds to a polyp; performing a forward wavelet transformation on the volume to obtain a set of wavelet coefficients, wherein each wavelet coefficient is associated with a length scale; determining, for each length scale, a transformation magnitude; and forming, for each length scale, a transformed set of wavelet coefficients associated with the length scale. An inverse wavelet transform is performed on the transformed wavelet coefficients for each length scale to obtain a reconstructed volume, and the reconstructed volume is analyzed for the existence of polyps.

CROSS REFERENCE TO RELATED UNITED STATES APPLICATIONS

This application is a Divisional Application of U.S. patent applicationSer. No. 10/915,077, filed on Aug. 10, 2004, which is fully incorporatedherein by reference.

This application claims priority from “Wavelet based detection of colonpolyps”, Provisional Patent Application No. 60/494,665 of SenthilPeriaswamy, filed Aug. 13, 2003, the contents of which are incorporatedherein by reference.

BACKGROUND OF THE INVENTION

The diagnostically superior information available from data acquiredfrom current imaging systems enables the detection of potential problemsat earlier and more treatable stages. Given the vast quantity ofdetailed data acquirable from imaging systems, various algorithms mustbe developed to efficiently and accurately process image data. With theaid of computers, advances in image processing are generally performedon digital or digitized images.

Digital acquisition systems for creating digital images include digitalX-ray film radiography, computed tomography (“CT”) imaging, magneticresonance imaging (“MRI”), ultrasound (“US”) and nuclear medicineimaging techniques, such as positron emission tomography (“PET”) andsingle photon emission computed tomography (“SPECT”). Digital images canalso be created from analog images by, for example, scanning analogimages, such as typical x-rays, into a digitized form. However, thelarge amount of data in digital images is generally difficult andtedious for a human, such as a physician, to interpret withoutadditional aid. Computer-aided diagnosis (“CAD”) systems play a criticalrole in aiding the human, especially in the visualization, segmentation,detection, registration, and reporting of medical pathologies.

Digital images are created from an array of numerical valuesrepresenting a property (such as a grey scale value or magnetic fieldstrength) associable with an anatomical location points referenced by aparticular array location. The set of anatomical location pointscomprises the domain of the image. In 2-D digital images, or slicesections, the discrete array locations are termed pixels.Three-dimensional digital images can be constructed from stacked slicesections through various construction techniques known in the art. The3-D images are made up of discrete volume elements, also referred to asvoxels, composed of pixels from the 2-D images. The pixel or voxelproperties can be processed to ascertain various properties about theanatomy of a patient associated with such pixels or voxels.

Once anatomical regions and structures are constructed and evaluated byanalyzing pixels and/or voxels, subsequent processing and analysisexploiting regional characteristics and features can be applied torelevant areas, thus improving both accuracy and efficiency of theimaging system.

One of the more critical CAD tasks includes the screening and earlydetection of various types of cancer from a volume data (e.g., a CTvolume data). For instance, cancers such as colon cancer have shown adecrease in mortality rates resulting from the early detection andremoval of cancerous tumors. Pathologies are typically spherical orhemispherical in geometric shape. In many cases, these sphere-likepathologies are attached to linear or piece-wise linear surfaces.Unfortunately, existing methods generally do not detect characteristicsymptoms of various cancers until the advanced stages of the disease.Therefore, a primary goal in advancing preventive cancer screening is toprovide for earlier detection of the characteristic symptoms.

SUMMARY OF THE INVENTION

In one aspect of the invention, a method of identifying colon polyps ina digital volume, wherein the volume comprises a plurality of valuescorresponding to a domain of points in a 3D space, is provided. Themethod includes selecting a mother wavelet scaling function thatcorresponds to a polyp, performing a forward wavelet transformation onthe volume to obtain a set of wavelet coefficients, wherein each waveletcoefficient is associated with a length scale, determining, for eachlength scale, a transformation magnitude, and forming, for each lengthscale, a transformed set of wavelet coefficients associated with thelength scale. The method also includes performing, for each lengthscale, an inverse wavelet transform on the transformed waveletcoefficients corresponding to said length scale, to obtain areconstructed volume, and analyzing said reconstructed volume for theexistence of polyps.

In a further aspect of the invention, transformation magnitude comprisesa multiplier magnitude, wherein the step of forming a transformed set ofwavelet coefficients includes multiplying, for each length scale, thewavelet coefficients by the multiplier for that length scale to from amultiplied coefficient set for said length scale and wherein said stepof performing an inverse wavelet transform is performed on saidmultiplied coefficient set for said length scale.

In a further aspect of the invention, the transformation magnitudecomprises a threshold magnitude, wherein the step of forming atransformed set of wavelet coefficients includes selecting, for eachlength scale, those wavelet coefficients whose magnitudes exceeds thethreshold for that length scale, to form a subset of waveletcoefficients associated with the length scale, and wherein said step ofperforming an inverse wavelet transform is performed on the coefficientsubset for the length scale.

In a further aspect of the invention, the transformation magnitudecomprises a threshold magnitude, wherein the step of forming atransformed set of wavelet coefficients includes selecting, for eachlength scale, those wavelet coefficients whose magnitudes exceeds thethreshold for that length scale, to form a template subset of waveletcoefficients associated with the length scale. The method furtherincludes the steps of performing a forward wavelet transform of a secondvolume, to obtain a second set of wavelet coefficients, comparing, foreach length scale, coefficients of the second set of waveletcoefficients with coefficients of a template subset for said lengthscale, wherein a match between the coefficients of the template subsetand coefficients of the second set of wavelet coefficients indicates thepresence of a polyp corresponding to the length scale.

In another aspect of the invention, a method of identifying colon polypsin a digital volume, wherein the volume includes a plurality of valuescorresponding to a domain of points in a 3D space, is provided. Themethod includes selecting a mother wavelet scaling function thatcorresponds to a polyp and performing a forward wavelet transformationon the volume to obtain a set of wavelet coefficients, wherein eachwavelet coefficient is associated with a length scale. For each lengthscale, a multiplier magnitude associated with that length scale is usedto multiply the wavelet coefficients for the same length scale to form amultiplied coefficient set for that length scale. For each set ofmultiplied coefficients, an inverse wavelet transform is performed toobtain a reconstructed volume, and the reconstructed volume is analyzedfor the existence of polyps.

In a further aspect of the invention, a method of identifying colonpolyps in a digital volume, wherein the volume includes a plurality ofvalues corresponding to a domain of points in a 3D space, is provided.The method includes selecting a mother wavelet scaling function thatcorresponds to a polyp and performing a forward wavelet transformationon the volume to obtain a set of wavelet coefficients, wherein eachwavelet coefficient is associated with a length scale. For each lengthscale, a threshold magnitude is determined so that those waveletcoefficients whose magnitudes exceeds the threshold for that lengthscale are selected to form a subset of wavelet coefficients associatedwith the length scale. For each subset of wavelet coefficients, aninverse wavelet transform is performed to obtain a reconstructed volume,and the reconstructed volume is analyzed for the existence of polyps.

In a further aspect of the invention, a method of identifying colonpolyps in a digital volume, wherein the volume includes a plurality ofvalues corresponding to a domain of points in a 3D space, is provided.The method includes selecting a mother wavelet scaling function thatcorresponds to a polyp and performing a forward wavelet transformationon the volume to obtain a set of wavelet coefficients, wherein eachwavelet coefficient is associated with a length scale. For each lengthscale, a threshold magnitude is determined to select those waveletcoefficients whose magnitudes exceeds the threshold, to form a templatesubset of wavelet coefficients associated with the length scale. Aforward wavelet transform of a second volume is performed to obtain asecond set of wavelet coefficients. For each length scale, coefficientsof the second set of wavelet coefficients are compared with coefficientsof a template subset for the length scale, wherein a match between thecoefficients of the template subset and the coefficients of the secondset of wavelet coefficients indicates the presence of a polypcorresponding to the length scale.

In further aspect of the invention, the method includes, prior toperforming the forward wavelet transform, calculating a first derivativeof the volume, and selecting the mother wavelet function to be similarto a first derivative of a polyp.

In another aspect of the invention, a program storage device readable bya computer, tangibly embodying a program of instructions executable bythe computer to perform the method steps for identifying colon polyps ina digital volume, wherein the volume includes a plurality of valuescorresponding to a domain of points in a 3D space, is provided.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1 a-b depict a flow chart of a preferred method of the invention.

FIG. 2 depicts a biorthogonal wavelet scaling function.

FIG. 3 depicts a 2D image of a polyp, the wavelet response of thatpolyp, and the original polyp overlaid with the wavelet response.

FIG. 4 depicts in the top row 3 orthogonal slices of a polyp subvolume,with the polyp located in the center, and in the bottom row, the waveletresponses for the corresponding slices.

FIG. 5 depicts an exemplary computer system for implementing a preferredembodiment of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Illustrative embodiments of the invention are described below. In theinterest of clarity, not all features of an actual implementation aredescribed in this specification. It will of course be appreciated thatin the development of any such actual embodiment, numerousimplementation-specific decisions must be made to achieve thedevelopers' specific goals, such as compliance with system-related andbusiness-related constraints, which will vary from one implementation toanother. Moreover, it will be appreciated that such a development effortmight be complex and time-consuming, but would nevertheless be a routineundertaking for those of ordinary skill in the art having the benefit ofthis disclosure.

While the invention is susceptible to various modifications andalternative forms, specific embodiments thereof have been shown by wayof example in the drawings and are herein described in detail. It shouldbe understood, however, that the description herein of specificembodiments is not intended to limit the invention to the particularforms disclosed, but on the contrary, the intention is to cover allmodifications, equivalents, and alternatives falling within the spiritand scope of the invention as defined by the appended claims.

A goal of this algorithm is to assist in the automatic detection ofpolyps in the colon. The input includes 3D scans of the colon, whosevalue can be, e.g., a magnetic field intensity, and the output includesa wavelet response volume. The response volume can then be used as afeature for detection/classification of the polyp. This idea can beutilized for various imaging modalities, such as PET, CT, MRI, etc.Prior to application of the methods of the invention the 3D volumetricimage can be preprocessed to identify structures of interest for furtheranalysis.

Basic Wavelets

Wavelets are function building blocks that can quickly decorrelate data.A given signal ƒ can be decorrelated by wavelets as follows:

$f = {\sum\limits_{i}{\gamma_{i}\varphi_{i}}}$where γ_(i) are wavelet coefficients and φ_(i) are wavelets. The waveletfunctions have the special property that they are derived from a motherwavelet function, and all other wavelet basis functions are scaled andtranslated versions of this mother function:

φ(x) = mother  wavelet φ_(i, k)(x) = φ(2^(l)x − k) scale = 2^(l)translation = 2^(−l)k${{f(x)} = {\sum\limits_{l,k}{\gamma_{l,k}{\varphi_{l,k}\left( {{2^{- l}x} - k} \right)}}}},$where the mother function can be selected to bring out a feature ofinterest in the signal ƒ. Note that wavelet basis functions and theirassociated coefficients are indexed by both length scale l andtranslation k. These wavelets are referred to as biorthogonal swavelets. The characteristic length scale associated with a wavelet ofscale index l decreases for increasing l.

Although wavelets are commonly defined in terms of the Fourier transformof a function, there exist alternative methods of calculating waveletbasis functions and their coefficients that do not rely upon Fouriertransforms. One such method well known in the art is known as thelifting scheme. The lifting scheme ensures fast calculation of theforward and inverse wavelet transforms that only involve finite impulseresponse filters. The transform works for images of arbitrary size withcorrect treatment of the boundaries, and all of the computations can bedone in-place without need of extra memory. Wavelets generated by thelifting scheme are particularly well suited to image analysis since animage is a bounded signal of finite length, as the lifting scheme doesnot introduced boundary artifacts.

In a preferred method of the invention, a mother wavelet scalingfunction is selected whose shape is similar to that of a polyp. Thewavelet generated by the lifting scheme are preferred because thescaling function has desirable properties and resembles the polyps, andthe wavelets can be computed efficiently (leading to a fastimplementation). One exemplary wavelet mother function issemi-spherically shaped. Then the wavelet response coefficients will bemaximized at the location of structures similar in size and shape to thescaling function. In general, a polyp volume can be transformed into thewavelet domain, and the wavelet coefficients can be interpreted toreflect the similarity of the polyp to the wavelet scaling function. Foran image I(x,y,z) of n points that maps R³→R, there can be n waveletcoefficients. These coefficients can then be analyzed to identifypotential polyps (candidate detection) or used as a feature todistinguish polyps from non-polyp structures.

First Embodiment Detection

After preprocessing the image, one can perform a forward waveletdecomposition of a volume of data points via, e.g., the lifting scheme,using an appropriate mother scaling function. Although the volume beinganalyzed can be an image volume, it need not be so and the volume datapoints can have other meanings, as will be discussed below. For ease ofexplanation, the embodiments described herein below will be described interms of an image. Referring now to FIG. 1 a, after obtaining a volumeof data points for analysis at step 101, one then selects a motherwavelet function at step 103, and performs the forward wavelet transformon the data volume at step 104. A first embodiment of the invention canbe used for the detections of polyps and other structures of interest.Assuming one started with an image comprising n points, one ends up witha set of n coefficients of varying length scales. A wavelet basisfunction whose shape and length scale correspond to a polyp (or cavity)will have a coefficient of much greater magnitude than a waveletcorresponding to a fold or other elongated structure of similar size.

A coefficient threshold can then be defined at step 111 for each scalecoefficient l based on the intensity: γ_(th)=2⁻¹β, where β represents athreshold intensity value, and that subset of m coefficients whosemagnitudes exceeds the threshold γ_(th) is then selected at step 112.For a first few times that this procedure is applied for detecting apolyp, β will be determined by inspection. However, once an appropriatevalue of β has been found, that value can be automatically applied infuture detection procedures. The intensity threshold γ_(th) isdetermined to eliminate noise at each scale. Note that the intensitythreshold increases for decreasing length scale l. This accounts for thefact coefficients are more sensitive to noise as the length scaledecreases.

The image can then be reconstructed from the subset of m coefficients atstep 113 using the inverse wavelet transform. The resultingreconstructed image will contain those regions suspected of being apolyp, which can then be analyzed at step 114 to detect the polyp. Thisprocess of determining a coefficient threshold for each scale value l,selecting a subset of coefficients exceeding that threshold, andreconstructing the image from that subset to find a polyp can beperformed for each length scale l. Thus, for each l, one obtains asubset S₁ of coefficients whose magnitude exceeds the threshold γ_(th).This repeated process enables one to detect polyps of different sizes.

Second Embodiment Enhancement

In a second embodiment of the invention, after suitable preprocessing,one can again start by performing a forward wavelet decomposition of animage of n points to obtain n basis functions and associatedcoefficients.

In this embodiment, rather than thresholding the coefficients, onedetermines at step 121 a fixed multiplier value that is dependent onscale: γ′₁=2⁻¹αγ₁, where α is a constant multiplier coefficient. Thewavelet coefficients are multiplied by this multiplier at step 122. Aswith the first embodiment, for the first few times that this procedureis applied for detecting a polyp, α will be determined by inspection.However, once an appropriate value of α has been found, that value canbe automatically applied in future enhancement procedures. One can thenreconstruct the volume at step 123 by using the inverse wavelettransform on the primed set of coefficients. The resulting volume wouldcontain those regions suspicious of being a polyp appearing enhanced orhighlighted due to the multiplication by α, and can be analyzed at step124. Examples are shown in FIGS. 2 and 3. Once again, this process canbe repeated for each length scale to find polyps of different sizes.

Third Embodiment Detection by Template Matching

In the third embodiment of invention, one seeks to detect a polyp in thewavelet domain rather than the spatial domain. Once again, aftersuitable preprocessing, one can start by performing a forward waveletdecomposition of an image of n points to obtain n basis functions andassociated coefficients. Turning now to FIG. 1 b, as in the firstembodiment, coefficient thresholds can be defined at step 131 for eachscale coefficient l based on the intensity: γ_(th)=2⁻¹β, where βrepresents a threshold intensity value, and that subset of mcoefficients exceeding the threshold γ_(th) is then selected at step132. This process is repeated to select a subset of coefficients T_(l)for each length scale l, and can also be repeated for differently shapedbasis functions.

These subsets of coefficients can then be used as templates fordetecting polyps as follows. Given another input image volume at step134, one can apply the forward wavelet transform to obtain another setof wavelet coefficients at step 135. One can then match this set ofwavelet coefficients with a template for a given l at step 136 to detecta polyp. For each value of l, one seeks a subset of wavelet coefficientsof the image being analyzed that match the coefficients in the templateset T_(l). By matching is meant that a wavelet coefficient of the imagebeing analyzed has the same translation and length scale indices as atemplate set coefficient of the same magnitude, or approximately samemagnitude. If, at step 137, every coefficient in a template set T_(l)can be associated in this manner to a coefficient of the image to beanalyzed, then a match has been found. Identification of such a subsetis indicative of the presence of a polyp whose size corresponds to thelength scale l of the template set T_(l). This technique of templatematching in the wavelet domain is quite robust with respect to noise andother structures.

A further variation of the invention is based on the fact that the firstderivative of a polyp has a unique signature that can be detected usingthe wavelet coefficients. This signature of a polyp is due to the factthat since a polyp is usually attached to an organ wall, it is usuallysemi-spherical in shape, as opposed to being filly spherical. Thecalculation of the first derivative of the image is performed at step102, prior to selecting the mother wavelet scaling junction andperforming the forward wavelet transform. Thus, in these embodiments,instead of applying the wavelet transform to the raw images, the wavelettransform is applied to the magnitude of the derivatives of the originalvolume. This variation can be utilized in each of the three embodimentsdiscussed above.

There are several advantages to using wavelets for the detection ofpolyps. Wavelets are multiscale: one can obtain an idea of the size of apolyp by looking at the response at various length scales. The wavelettransform can be computed in-place, and is thus memory efficient.Furthermore, the transform is linear in the number of voxels, and isthus computationally efficient to calculate.

Note that the methods presented herein can be easily extended fromfinding solid shapes to finding holes or missing shapes in a substrate.In addition, these methods can be applied to not just the imaged volume,but also to alternative volumes created, for example, by filtering.

It is to be understood that the present invention can be implemented invarious forms of hardware, software, firmware, special purposeprocesses, or a combination thereof In one embodiment, the presentinvention can be implemented in software as an application programtangible embodied on a computer readable program storage device. Theapplication program can be uploaded to, and executed by, a machinecomprising any suitable architecture.

Referring now to FIG. 5, according to an embodiment of the presentinvention, a computer system 501 for implementing the present inventioncan comprise, inter alia, a central processing unit (CPU) 502, a memory503 and an input/output (I/O) interface 504. The computer system 501 isgenerally coupled through the I/O interface 504 to a display 505 andvarious input devices 506 such as a mouse and a keyboard. The supportcircuits can include circuits such as cache, power supplies, clockcircuits, and a communication bus. The memory 503 can include randomaccess memory (RAM), read only memory (ROM), disk drive, tape drive,etc., or a combinations thereof The present invention can be implementedas a routine 507 that is stored in memory 503 and executed by the CPU402 to process the signal from the signal source 508. As such, thecomputer system 501 is a general purpose computer system that becomes aspecific purpose computer system when executing the routine 507 of thepresent invention.

The computer system 501 also includes an operating system and microinstruction code. The various processes and functions described hereincan either be part of the micro instruction code or part of theapplication program (or combination thereof) which is executed via theoperating system. In addition, various other peripheral devices can beconnected to the computer platform such as an additional data storagedevice and a printing device.

It is to be further understood that, because some of the constituentsystem components and method steps depicted in the accompanying figurescan be implemented in software, the actual connections between thesystems components (or the process steps) may differ depending upon themanner in which the present invention is programmed. Given the teachingsof the present invention provided herein, one of ordinary skill in therelated art will be able to contemplate these and similarimplementations or configurations of the present invention.

The particular embodiments disclosed above are illustrative only, as theinvention may be modified and practiced in different but equivalentmanners apparent to those skilled in the art having the benefit of theteachings herein. Furthermore, no limitations are intended to thedetails of construction or design herein shown, other than as describedin the claims below. It is therefore evident that the particularembodiments disclosed above may be altered or modified and all suchvariations are considered within the scope and spirit of the invention.Accordingly, the protection sought herein is as set forth in the claimsbelow.

1. A method of identifying colon polyps in a digital volume, whereinsaid volume comprises a plurality of values corresponding to a domain ofpoints in a 3D space, said method comprising the steps of: selecting amother wavelet scaling function that corresponds to a polyp; calculatinga first derivative of said volume and selecting the mother waveletfunction to be similar to a first derivative of a polyp; performing aforward wavelet transformation on said volume to obtain a set of waveletcoefficients, wherein each wavelet coefficient is associated with alength scale; determining for each length scale, a transformationmagnitude, wherein the transformation magnitude comprises a thresholdmagnitude; forming, for each length scale, a transformed set of waveletcoefficients associated with said length scale, wherein said formingcomprises selecting, for each length scale, those wavelet coefficientswhose magnitudes exceeds the threshold for said length scale, to form asubset of wavelet coefficients associated with said length scale;performing, for each length scale, an inverse wavelet transform on thetransformed wavelet coefficients corresponding to said length scale, toobtain a reconstructed volume, wherein said performing an inversewavelet transform is performed on said coefficient subset for saidlength scale; and analyzing said reconstructed volume for the existenceof polyps.
 2. A method of identifying colon polyps in a digital volumewherein said volume comprises a plurality of value corresponding to adomain of points in a 3D space said method comprising the step of:selecting a mother wavelet scaling function that corresponds to a polyp;calculating a first derivative of said volume and selecting the motherwavelet function to be similar to a first derivative of a polyp;performing a forward wavelet transformation on said volume to obtain aset of wavelet coefficients, wherein each wavelet coefficient isassociated with a length scale; determining, for each length scale, athreshold magnitude; selecting, for each length scale those waveletcoefficients whose magnitudes exceeds the threshold for said lengthscale, to form a subset of wavelet coefficients associated with saidlength scale; performing, for each length scale, an inverse wavelettransform on the coefficient subset corresponding to said length scale,to obtain a reconstructed volume; and analyzing said reconstructedvolume for the existence of polyps.
 3. A program storage device readableby a computer, tangibly embodying a program of instructions executableby the computer to perform method steps for identifying colon polyps ina digital volume, wherein said volume comprises a plurality of valuescorresponding to a domain of points in a 3D space, said methodcomprising the steps of: selecting a mother wavelet scaling functionthat corresponds to a polyp; calculating a first derivative of saidvolume and selecting the mother wavelet function to be similar to afirst derivative of a polyp; performing a forward wavelet transformationon said volume to obtain a set of wavelet coefficients, wherein eachwavelet coefficient is associated with a length scale; determining foreach length scale, a transformation magnitude, wherein thetransformation magnitude comprises a threshold magnitude; forming, foreach length scale a transformed set of wavelet coefficients associatedwith said length scale, wherein said forming comprises selecting, foreach length scale, those wavelet coefficients whose magnitudes exceedsthe threshold for said length scale, to form a subset of waveletcoefficients associated with said length scale; performing, for eachlength scale, an inverse wavelet transform on the transformed waveletcoefficients corresponding to said length scale, to obtain areconstructed volume, wherein said performing an inverse wavelettransform is performed on said coefficient subset for said length scale;and analyzing said reconstructed volume for the existence of polyps.